Electrical analog model for fluid flow transmission system

ABSTRACT

An electrical analog model for simulating fluid flow characteristics in a pipeline flow system, such as a gas transmission system, wherein the analog includes a source of electrical voltage proportional to inlet fluid pressure, a compressor station analog, a plurality of pipeline section analogs, a regulator station analog, and a flow transient or load utilization simulator. The compressor station analog includes a capacitor pump, a source of alternating current for driving the capacitor pump, a controlled-level amplifier for controlling the drive to the capacitor pump, and a differential amplifier responding to changes in the output of the capacitor pump and driving the controlled level amplifier. Each line section analog is a delay line including a nonlinear resistance element, such as a field effect transistor having a resistance proportional to the current passing through it, and a nonlinear voltage variable capacitance diode having a capacitance proportional to the inverse square root of impressed voltage. The regulator analog is a voltage regulator including a control element, such as a field effect transistor, and a differential amplifier responding to changes in regulator analog output voltage to drive the field effect transistor. The transient and load utilization simulator includes a function generator programmed by an opaque tape to simulate fluid withdrawal. The tape controls the amount of light between a light source and a light sensor which produces an output current in response to light. The output current produced is impressed on the electrical analog system by a flow modulator, such as by modulating the regulator station output with this current.

United States Patent [72] Inventors Glenn Damewood;

Cecil R. Sparks; James D. King, all of San Antonio, Tex. [21] Appl. No.741,528 [22] Filed July 1, 1968 [45] Patented May 25, 1971 [73] AssigneeSouthern Gas Association San Antonio, Tex.

[54] ELECTRICAL ANALOG MODEL FOR FLUID FLOW TRANSMISSION SYSTEM 18Claims, 4 Drawing Figs. [52] US. Cl 235/184, 235/197, 307/229, 328/142,333/29 [51] Int. Cl 606g 7/57, H03h 7/36 [50] Field of Search 235/184,197; 307/229, 237, 304, 320; 328/142; 333/29 [56] References CitedUNITED STATES PATENTS 3,146,346 8/1964 Evangelisti et a1 235/1843,191,130 6/1965 Rudd et al. 307/320X 3,207,889 9/1965 Evangelisti etal.. 235/184 3,260,968 7/1966 Drapkin 333/29 3,404,263 10/1968Williams... 235/197X 3,404,266 10/1968 Woodley 235/197 3,393,369 7/1968Embley et al. 235/197X 3,396,267 8/1968 Dietrich 235/184X 3,492,497l/l970 Gilmour et a1 235/197X OTHER REFERENCES R, M. Searing: Variablecapacitance Diodes used as Phase Shift Devices Proceedings of the lre;March 1961 pages COMPRESSOR ANALOG FUNCTION GENE/PA r01? I I I I I I IPrimary Examiner-Eugene G. Botz Assistant ExaminerFelix D. GruberAttorney-Hyer, Eickenroht, Thompson and Turner ABSTRACT: An electricalanalog, model for simulating fluid flow characteristics in a pipeline:flow system, such as a gas transmission system, wherein the analogincludes a source of electrical voltage proportional to inlet fluidpressure, a compressor station analog, a plurality of pipeline sectionanalogs, a regulator station analog, and a flo'w transient or loadutilization simulator. The compressor station analog includes acapacitor pump, a source of alternating current for driving thecapacitor pump, a controlled-level amplifier for controlling the driveto the capacitor pump, and a differential amplifier responding tochanges in the output of the capacitor pump and driving the controlledlevel amplifier. Each line section analog is a delay line including anonlinear resistance element, such as a field effect transistor having aresistance propor tional to the current passing through it, and anonlinear voltage variable capacitance diode having a capacitanceproportional to the inverse square root of impressed voltage. Theregulator analog is a voltage regulator including a control element,such as a field effect transistor, and a differential amplifierresponding to changes in regulator analog output voltage to drive thefield effect transistor. The transient and load utilization simulatorincludes a function generator programmed by an opaque tape to simulatefluid withdrawal. The tape controls the amount of light between a lightsource and a light sensor which produces an output current in responseto light. The output current produced is impressed on the electricalanalog system by a flow modulator, such as by modulating the regulatorstation output with this current.

e6 ELEMENT P/PEA/A/E SECT/OA/ E'fGZ/LATOI? 57ZlT/0/V A N4 L06 ANALOG F La w MODULA m2 -41 AMPLIFIER ELECTRICAL ANALOG MODEL FOR FLUID FLOWTRANSMISSION SYSTEM This invention relates to electrical analogs and, inone of its aspects, to an electrical analog and method for simulatingflow characteristics in pipeline systems, such as a natural gasdistribution or transmission system, including the effect of flowtransients of such flow. In another aspect, it relates to an analog ofthe component parts of a fluid transmission system for use in anelectrical analog thereof, such as a regulator station analog, pipelinesection analog and a compressor station analog. In another aspect, itrelates to apparatus for simulating flow transients and load withdrawaldemands on a pipeline system and for impressing such transients demandson an electrical analog of such a system.

Many pipeline systems, such as cross-country natural gas transmissionpipelines, transport fluid under pressure to various users through milesof pipeline, and sometimes through 'several intermediate compression andregulation stages. The

amount of gas required by these users, for example a large metropolitangas company distribution system, will vary a great deal so that thetransmission system is constantly subjected to a varying load. Theresult of varying load and other conditions which deviate fromsteady-state flow is that the fluid system is subjected to flowtransients, and these flow transients affect the flow of fluidthroughout the system. In order to optimize flow throughout the systemand thus provide efficient and economical fluid transportation, somemeans must be provided for giving analytical data on the effects ofknown or predicted flow transients on this flow.

Although there have been analytical solutions which are adequate forsteady-state fluid flow computation, the problem of transient pipelineflow has historically defied solution on a rigorous analytical basis.With the advent of high speed computational devices, however, solutionof this transient flow problem has become possible. However, thesedevices, such as digital or analog computers, involve solution of thenonlinear pipeline transient flow equations and, thus, require highlysophisticated and expensive electronic equipment, and highly skilledpersonnel.

It is, thus, an object of this invention to provide a system and methodfor defining transient flow characteristics without the necessityofsolving the complex flow equations describing transient flow. Anotherobject is to provide such a system and method which uses relativelysimple and inexpensive electronic equipment and does not require theattention of highly skilled personnel.

Another object is to provide such a system and method which employs anelectrical analog model of fluid flow system so that measurement ofelectrical quantities, such as voltage or current, in the analog modelprovides information about the flow quantities of the fluid systemduring both steady-state and transient flow conditions.

It is another object to provide such an analog in which each of thecomponent parts of the fluid system and the transient coupling betweenthese parts is simulated.

Other objects, advantages and features of this invention will beapparent to one skilled in the art upon consideration of the writtenspecification, the appended claims, and the attached drawings, wherein:

FIG. 1 is a block diagram of an illustrative natural gas pipeline systemto be simulated;

FIG. 2 is a block diagram of an electrical analog of the pipeline systemof FIG. 1;

FIG. 3 is a more detailed block and schematic diagram of the analogsystem of FIG. 2 showing the component parts of the system; and

FIG. 4 is a schematic diagram of the analog systems of FIGS. 2 and 3 andthe component parts thereof.

In accordance with this invention, a pipeline system, such as a gasdistribution or transmission system, is simulated by an electrical modelor analog system wherein electrical quantities, such as voltage orcurrent throughout the analog system simulate corresponding flowquantities throughout the fluid system. Component parts of the fluidsystem are each individually simulated by electrical simulators andthese are in terconnected in a manner analogous to the fluid system.Flow transients are simulated by generating an electrical signalproportional thereto and the impressing this signal on the electricalmodel or analog so that the electrical quantities of the electricalanalog are affected in a manner analogous to the way that flowtransients affect the flow quantities of the fluid system. Thus, thepresent invention provides adequate data on both transient andsteady-state flow conditions without the necessity of solving thecomplex flow equations, by the use of a relatively inexpensive andeasilyconstructed electronic simulator or analog model which simulatesactual pipeline transient response on a physical basis. Also, thesimulator can be operated and maintained by persons of moderate skills.

Referring to the drawings, in FIG. 1, a typical pipeline transmissionsystem for natural gas is illustrated. Of course, the invention isequally applicable to other pipeline systems for transporting otherfluids and also to distribution systems. Gas at pressure P1 enters theupstream end of the system from a storage reservoir or adjoiningpipeline (not shown) through an inlet 10 and if pressure P1 is below thedesired pressure for satisfactory transportation of the gas, it is thenconducted to a compressor station 11. The compressor station functionsto raise pressure P1 to a suitable pressure for transportation, such asthe discharge pressure P2. Gas is then conducted from the compressordischarge at pressure P2 through a pipeline 12 which is illustrated as24 miles in length. The gas undergoes a pressure drop through pipeline12 to pressure P3 and a further pressure drop to pressure P4 which isagain at a pressure insufficient for satisfactory operation. Asillustrated, gas at pressure P3 may be discharged through a. valve 13 toa regulator station 14 and thus to a load 15. Regulator station 14functions to provide a constant lower pressure P3 to load 15 despitevarying withdrawal rates.

At the termination of pipeline 12, gas at pressure P4 enters a secondcompressor station 16 and the gas pressure is then raised to a pressureP5 suitable for continuing transportation through a pipeline 17, whichis illustrated as 30 miles in length. As the gas flows through pipeline17, it undergoes an additional pressure drop to a pressure P6 and entersa regulator station 18. This regulator station functions to maintain anoutput pressure P7 to a load 19 despite varying withdrawal rates. Theloads 15 and 19 may be metropolitan gas distribution systems or otherloads for utilizing the gas.

DEVELOPMENT OF THE ANALOGY Before an electrical analog model can bedeveloped for the transmission system of FIG. 1 or any fluid flowsystem, it is necessary to develop the analogies between electricalquantities, and the passage of electrical current through the electricalmodel, and fluid flow quantities and the passage of fluid through thefluid system. These analogies have been derived by comparing themathematical equations governing dynamic fluid flow and electricalcurrent flow through a given electrical circuit until equations ofequivalent form are found. Certain variables in the electrical equationcan then be used\ to represent corresponding variables in the fluid flowequations. Generally, several different analogies can be set up in thismanner, but one set of analogies will probably be found most convenientto work with and require the simplest electronic circuitry. The complexnonlinear equations obtained need not be solved, but only written inincremental form.

By way of illustrationof the development of such an analogy and theelectrical analog model based on the chosen analogy, reference willhereinafter be made to the flow of natural gas through the pipelinedistribution system illustrated in FIG. 1. Similar techniques can beutilized in developing analogies and an electrical analog model forother fluid flow -systems.

The equations for one-dimensional, isothermal, compressible pipe flowcharacteristic of most pipelines transporting gaseous media aremathematically-nonlinear and cannot be solved analytically. Theseequations have been found to be:

22 BK: "r 1 p= RTZ Where p fluid pressure p fluid density V= fluidvelocity R gas constant, l535/mol. wt.

f pipe friction factor T= fluid temperature Z fluid compressibilityfactor D= pipeline diameter (id) 3 acceleration constant x= distancealong the pipe t= time Equation (1) is the equation of motion and thefirst two terms may be considered as the gradient of total pressure(static plus dynamic) along the pipeline, the third is the rate ofchange of momentum or inertial term, the fourth is pipe frictional loss,and the fifth is an elevation profile term. Equation (2) is the equationof continuity and equation (3) is the equation of state for the gaswhich must be taken into account due to the nonideal character of thegas.

When applying suitable simplification of these basic equations to thecase of steady-state flow, they can be integrated to provide rigidsolutions. However, this is not the case when they are applied topipeline transient flow solutions. When applied to the transient flowcase, the term JELLO Since equations (la), (2), and (3) cannot beintegrated to provide an exact solution to the transient flow problem inclosed form, a special computational technique, such as the electricalanalog model, must be used.

Now, defining weight rate of mass flow as m so that m=p VA (where A areaand V= average fluid velocity in the pipeline (4) and by using equation(3) to transform p to p in equations '12:) and (5), these equationsbecome, respectively:

g2 m f R TZ dz 1 Q A and d A d .1. dx RTX dt 0 (6) These equationsdescribe the dependency of line pressure gradient on pipe friction, andthe dependency of transients flow on line pack variations.

It has been found that the equations describing electrical delay linesare of equivalent form. For example, delay line equations of motion andcontinuity are:

de di dz dt Where L inductance per unit length dx, (henries) C=electrical charge per unit length dx, (coulombs) R Resistance per unitlength dx, (ohms) e Voltage 1' Current As previously stated, for mostproblems involving long, crosscountry pipelines, the inertial terms inEquation (1) viz., apV lat, may be assumed zero. Therefore, theelectrical inductance L can be neglected in the analog, and any lengthof pipe length I can be simulated by an electrical R-C network. Further,greater lengths of pipe can be simulated by coupling multiple sectionsof this basic R-C delay line section. Thus, where a natural gas pipelineis analoged, equation (7) can be rewritten as:

Assume the following analogies for simulating pipeline pressure at apoint along the pipeline and mass flow: P man where:

p=pipeline fluid pressure e=voltage, delay line to ground i= current 1mai Using set of analogies (A) in which voltage (2) is proportional tothe square of pressure (p and current (i) proportional to mass flow (m)and considering the lumping factor and the time speed up from real timeto analog time, the following conversion factors can be chosen whichwill define the relationship between the electrical quantitiesthroughout the analog to corresponding fluid system quantities:

=feet of pipeline per section analog time real time e spee up) Thesefactors can be selected to give a convenient and workable relationshipbetween the electrical quantity and corresponding fluid quantity,depending on, for example, the ranges of pressures and fluid flowinvolved and the maximum voltages and current for the electricalcircuitry used.

Inserting these factors in the pipeline equations (5) and (6), thesebecome which are in equivalent form to the delay line equations (7a) and(8), thus where R =a Constant C =a Constant Using analogy (B) in whichvoltage (e) is proportional to the pressure (p) and current (i) isproportional to mass flow (m), then the requirements for Ri and C iwould be expressed as follows:

RI=RO e C =Co (14) In choosing one of these sets of analogies over theother, a variety of considerations are important. First, considerationmust be given to the relationship of operating voltages and currents tothe size of electrical components required for an analog with a usabletime scaling factor, that is a workable relationship between analog timeand real time. It has been shown, however, that the practicalconsiderations involved wouldpermit the use of reasonably sizedcomponents, voltages and currents with either set of analogies, andthus, the ultimate selection of analogies depends primarily upon thefollowing considerations:

1. The practicality and ease of evolving and building the circuitryrequired for obtaining proper resistance and capacitance effects for thepipe sections.

2. The ease and practicality of evolving proper compressor stationcharacteristics for each set of analogies.

3. The ultimate usefulness of the evolved analog to the industry (as forexample, the ease by which data may be interpreted).

4. The cost involved in fabricating the circuitry for either set ofanalogies in sufficient quantity for simulating a complete pipelinesystem.

and

ELECTRICAL MODEL OF THE PIPELINE-PIPELINE SECTION ANALOGY The p 2 e andm i analogy has been chosen to illustrate the application of thisinvention and the development of an electrical model. The electricalcircuitry used must provide the required nonlinear R & C values asdefined by Equations (11) and (12), and, thus, provide a rigorouselectrical analog of a pipe section in that its electrical conductive orresponse characteristics are directly analogous to the flowcharacteristics of a pipeline. An electrical delay line utilizingnonlinear R-C sections can be coupled to a load corresponding to theload that the fluid piping system to be analoged is connected to, andresponse of the electrical delay line section to its load willcorrespond to flow response of pipe section, within the accuracylimitations of the assumptions made. Further, complex piping networks ormeshes may be simulated by building analogous electrical meshes usingthe delay line elements.

Referring to FIG. 2, line section analogs Z0a-20i are shown as connectedin series or lumped together to simulate pipelines l2 and I7. Eachanalog 20 comprises the necessary nonlinear R-C circuitry and isillustrated as representing 6 miles of corresponding pipelinev The 6miles represent the number of miles per section of analog circuitry tobe used and, although the lumping length requirements of any system willvary, it has been found that a lumping length shorter than aboutone-tenth wave length of the highest frequency transient of interestgives best results. The transient propogation velocity in the nonlineardelay lines 20 is frequency-dependent.

Thus, the analog sections 20 each function as means for electricallysimulating the flow of fluid through a portion of the pipeline. Asillustrated in FIG. 3, each section 20 is preferably an R-C delay lineincluding a nonlinear resistance means 21, the resistance of which isproportional to the current passing through it, and a nonlinearcapacitance means 22, the capacitance of which is inversely proportionalto the square root of impressed voltage. As illustrated in FIG. 4, thenonlinear resistance means 21 may include a field effect transistor Q1which is biased to operate in the desired region by a potential derivedfrom a battery B1. A potentiometer P1 connected across battery Bl allowsadjustment of the bias point. The operation of O1 is based on theinherent characteristics of the source to drain resistance of the fieldeffect transistor which, over a wide range of current, varies to a veryclose approximation as a direct function of the current. PotentiometerP1 is set to make the source to drain resistance exactly correct for aparticular current in the operating range desired. Variations about thispoint are adequately exact to simulate the desired resistance variationas a function of current to the accuracy required in practice.

The addition of a diode D1 and a resistor R1 across Ql improves therange over which the characteristic of the resistance of P1 follows thedesired equations. This is obtained by making use of the inherentvariation of the diode internal impedance as a function of current. Theresistor R1 sets the minimum impedance in the branch of the circuitshunting the field effect transistor.

Also, as illustrated in FIG. 4, the nonlinear capacitance means 22 mayinclude a capacitive element C1 which is a semiconductor diode junctionexhibiting a capacitance which is a function of the applied voltage.Such semiconductor devices are available with specified capacitance vs.voltage characteristics under names of Vari-caps, varactors, voltagevariable capacitors, variable capacitance diodes and others. Thejunction capacitance of the devices is given by the relation Where C=capacitance at a voltage e C0= capacitance at a particular voltage k afactor usually between 1/3 and 1/2 dependent onjunction formationtechnique By choosing a device with k l/2, the criteria of Equation (12)is met and the capacitance will vary as the inverse square root of theline voltage.

Versatility in operating the analog section 20 is afforded both by theproper selection of analog factors and by electrical adjustments. Analogconversion factors may be selected such that a given delay line may beused to simulate virtually any size pipeline, while the electricaladjustment can be used to select optimum operating range and adjustelectrical operating curves for best fit to theoretical values. Theresistance curve may normally be adjusted within t 5 percent over a current range of two to one. The typical range of currents used in testingto date on an analog line system varied from about 6 ya to 35 m. Whenthe DC current is adjusted to around 22 a, the sections 20 have anaccurate (Spercent) response from about 15 to 30 ya; this 5 percentrefers to correctness of slope of the voltage-drop versus current plottalten on an x'y recorder. However, actual measurements on the analogwhen coupled as a pipeline system showed that rather wide deviations inelectrical performance curves caused negligible changes in transientpipeline response. Typical capacitance curves show that the theoreticalcurve on capacitance vs. voltage is achieved within percent over avoltage range of four to one. Actual adherence to theoretical curves, ofcourse, depends upon the individual semiconductor devices selected.

COMPRESSOR STATION ANALOG In evolving an adequate analog of a compressorstation to be used as part of an electrical analog model of the wholegas transmission system, the following conditions must prevail:

a. The compressor analog must be compatible with other analog componentssuch as pipe sections, regulators, etc.;

b. It must maintain proper termination impedance for the line sectionanalogs to which it is connected;

c. The analogous mass flow through the compressor analog must becontinuous, as mass flow through a compressor is contmuous;

d. The differential pressure or pressure head across the compressorstation analog must adequately represent the pressure head experiencedon the parent fluid system;

c. The compressor station analog must be programable or controllablewith the same dispatching or control orders as the actual station. Thiscontrol aspect requires that the pressure and flow analogies bepreserved and controlled in a predictable manner on a basis of fluid andcompressor parameters such as bore, stroke, speed, pressure, clearance,horsepower, volume, etc.

The compressor analog disclosed herein is based upon a step-by-stepanalog of a compressor cylinder cycle, coupled with controlled circuitryto program or control pumping characteristics in a manner analogous tothe way that an actual compressor would be controlled or programmed. Toachieve this total compressor station analog, the capacitor pumpdescribed in U.S. Letters Patent 2,951,638 issued to John V. Hughes andWilliam V. Rollwitz on Sept. 6, I960, is used to simulate the basiccycling action of a reciprocating compressor, and additional circuitryis added to afford appropriate control and programming capabilities. Itis not necessary to simulate the pulsation or high frequency flowtransients produced by the reciprocating action of compressor cylinders,and thus performance of the total compressor stations can be adequatelysimulated by using one equivalent compressor cylinder analog. In such anapplication, the single capacitor pump and associated circuitry wouldserve as the analog of an entire compressor station.

The capacitor pump alone will adequately simulate a station under longterm steady state (nontransient) flow conditions, since under'theseconditions suction pressure and discharge pressure would be steady.

However, in order to evolve an effective compressor analog controlsystem, it is essential that recognition be given to the controlphilosophy used at the actual compressor site to be simulated, which,generally, is to maintain constant discharge pressure regardless ofsuction pressure or station thru-put (flow rate). This is achieved byvarying compressor speed, clearance, horsepower, and number of cylindersin service. By maintaining constant discharge pressure just belowpressure rating of the pipeline, operation of the pipeline is maintainedat optimum efficiency without overstressing the pressure vessels andpiping. The analog control system to be described is designed such thatany drop in discharge pressure below the desired set point immediatelyincreases the drive applied to the capacitor pump. The design of thecapacitor pump is characterized by its ability to increase thru-put withincreases either in the amplitude or frequency of the voltage signalwhich drives the capacitor pump, as explained below.

Referring to FIGS. 3 and 4, the compressor station analog 23 is shown asincluding capacitor pump 24. Capacitor pump 24 includes series connecteddiodes Da and Db, the anode of Da functioning as an input for voltageproportional to suction pressure, the cathode of Db as an output forvoltage proportional to discharge pressure. A capacitor Ca is connectedto diodes Da and Db to form a T-section. The capacitor is driven by avariable amplitude alternating current signal and the amplitude andfrequency of the driving signal to capacitor Ca controls the outputvoltage of diode Db. The driving signal is generated by an AC signalgenerator 25.

Means is provided for conducting the driving signal to capacitor Ca andfor responding to changes in the voltage at the output of diode Dbcorresponding to changes in compressor discharge pressure to cause thedriving signal to vary in amplitude an amount sufficient to maintain theoutput voltage proportional to compressor discharge pressure. In FIG. 4,this means includes a differential amplifier 26 in which the diode Dboutput voltage (e5) is compared with a reference voltage (er). Thereference voltage is set by a potentiometer P2 which is connected from avoltage source to ground. The reference voltage is generally set to avalue proportional to the discharge pressure to be maintained at thecompressor station. Any difference between the output (2 5) andreference voltage (er) results in an error signal which is amplified inamplifier 26. This signal is then further amplified and its levelcontrolled by a controlled level amplifier 27 consisting of transistorsQ2- -Q7 and their associated components. The error signal is amplifiedby transistors Q3Q5 and then conducted to a symmetrical clipper circuit28 which consists of transistors Q6 and Q7 and their associatedcomponents. This circuit of O6 and Q7 has the property that itspeak-to-peak output level is determined by the operating voltageappearing at point (2) in FIGS. 3 and 4, provided the AC signalgenerator 25 output level is greater than the required output. Theoutput of the symmetrical limiter goes to transistor Q2 where it isamplified and is then conducted to the compressor cylinder analog 24 andcapacitor Ca. Thus, amplifier 27 operates to maintain the dischargevoltage equal to the reference voltage by controlling the peak-to-peaklevel of the AC drive signal through the symmetrical clipper in responseto the error signal from amplifier 26.

Feedback elements resistor R2 and capacitor C2 are connected in parallelfrom the reference signal input to the output of amplifier 26 and,together with resistors R3 and R8 and potentiometer P2 control the gainand frequency response of amplifier 26. This frequency response must besuch that the capacitor pump driving signal is properly attenuated inthe controlled level amplifier 27. Thus, the AC signal generatorfrequency must be much higher than the highest frequency required tosimulate the dynamic flow variations. Resistor R5 and capacitor C3 areparallel connected between diode Db output and amplifier 26 input toprovide phase correction and improve stability. A resistor R4 and diodeD2 are connected in the output circuit of amplifier 26 to preventcircuit malfunction and Iock-up under conditions of input signals thatwould cause the output from amplifier 26 to be positive. The othercomponents in controlled level amplifier 27 are connected in aconventional manner and are used to perform normal circuit functions.

Also, the discharge pressure from the compressor analog may be made tofollow a desired dynamic program by feeding a dynamic voltage signalinto the reference signal input of amplifier 26 through jack jl. Thedynamic voltage so applied is added to that from the potentiometer P2 tomake the reference to amplifier 26 the sum of the two.

Other variations of the compressor analog control philosophy would be tocontrol the pumping voltage by making use of a variable gain voltageamplifier instead of the symmetrical limiter 28. Another variation couldbe obtained by controlling the pumping oscillator frequency by thedifferential amplifier output.

REGULATOR STATION ANALOG In FIGS. 2, 3 and 4 the regulator station isshown as simulated by regulator station analogs 29 and 30, respectively.In electrical terms, the regulator analog functions to drop voltage froma value proportional to regulator station input (or pipelinetermination) pressure (P6) to a constant value proportional to regulatorstation output (P7). The circuitry employed must prevent variation inoutput voltage for variations in either or both the output current andinput voltage provided the latter is greater than the output voltage.Another requirement that the circuit must meet is that the outputcurrent magnitude must be equal to the input current.

Referring to FIG. 3, the regulator station analog 30 is shown asincluding a series control element 31 connected between the analogpipeline section and a load and a difference amplifier 32 which comparesthe element 31 output voltage level e7 with a reference voltage andamplifies the difference to control the voltage drop across the seriesregulating element. By use of sufficient gain, the voltage drop in theseries element 31 can be made to be that required to keep the outputvoltage extremely close to the reference voltage.

In FIG. 4 a circuit diagram of one possible embodiment of the regulatorstation analog is shown. A field effect transistor O8 is used as theseries element to minimize the flow of current in the control electrodeand insure continuity of current flow between input and outputterminals. A field effect transistor O9 is also used as the input stageof the differential amplifier 32 to minimize the current required fromthe line for sensing. In this manner the output current of the regulatoranalog is maintained equal to the input current. The reference voltageis set by a potentiometer P3 connected in a voltage divider (includingresistors R9 and R10) across a source of voltage. A selected portion ofQ8 output voltage (e7) is applied to the gate electrode G of Q9 and thereference voltage is applied to the source s of Q9. Differences betweenthe reference and output voltages results in an error signal which isamplified in Q9 and further amplified in transistors Q10 andQll of thedifferential amplifier circuit. The potential appearing at the collectorof 010 is connected through a resistor network including resistors R11and R12 to the gate electrode of Q8. The potential on the gate ofQ8.controls the impedance between its source and drain electrodes andthus can control the voltage drop between the input and outputterminals. The circuit operates in such a manner that any change thatwould tend to vary the output voltage causes the gate potential of O8 tovary in such a manner that the internal impedance is adjusted tomaintain the output voltage constant. The output voltage may be adjustedto any desired value by setting potentiometer P3 to provide theappropriate reference potential.

A similar electrical analog 29 could be developed to simulate regulatorstation 14. The valve 13 could be simulated electrically by an on-offswitch SW1 as shown in FIG. 2.

FLOW TRANSIENT AND LOAD SIMULATOR The primary object of this inventionis to study the effects of flow and load transients on the flow of fluidin a fluid flow system, as well as static flow. Thus, where anelectrical analog model is used, some means must be devised forsimulating electrically the flow transients that the parent flow systemis subjected to and then subjecting the electrical model to electricaltransients in a manner analogous to the manner in which the flow systemis subjected to flow transients. As illustrated in FIGS. 2, 3 and 4,load utilization and flow transients may be simulated by a load functiongenerator 33 which, in the preferred embodiment illustrated, is acombination electricalmechanical-optical device which can be programmedto generate virtually any voltage time function (wave shape) desired tosimulate load utilization. In FIG. 3, a transparent cylinder 34 isrotated by a motor 35. The cylinder 34 carries a mask of opaque material36 representative of the function to be generated. Strips of opaque tapeof the desired length and width may be used to give the desiredfunction. The cylinder 34 is rotated by motor between a light source 37and a photocell or light sensor 38. Light from the source 37 is focusedand collimated by passing it through collimating lenses 39 and slit 39::corresponding in width to the tape strips used. Light then passesthrough the mask region 36 and falls on photocell 38 which produces anelectrical output proportional to the amount of light transmittedthrough the mask 36. The motor 35 speed may be varied to control thetime rate of change of a function so that a time-varying electricalsignal may be generated of predetermined shape or spectrum. This signalis amplified by an amplifier 40 which is shown in detail in FIG. 4, andis used as the function signal in the analog system.

The electrical analog signal of the model of FIG. 2 is subjected to thefunction signal by modulation in a manner analogous to the way theparent flow system is subjected to transients. A flow modular 41, whichis a voltage-controlled impedance device, is used to modulate the analogsignal current. For example, it may modulate the output of the analogfor controlling current withdrawal from the delay line system. Theimpedance of the flow modulator is controlled by the sum of a dynamicvoltage signal from the load function generator and the setting ofpotentiometer P3 of FIG. 4 and transcribes this signal to actual currentloading of the delay line system. For example, if a sinusoidalmodulation of the current (analogous flow) is desired from the delayline, a sinusoidal voltage signal is introduced into the flow modulator.This signal results in a sinusoidal variation of load impedance, and,since this impedance is connected to a regulated (steady) volt- .age, asinusoidal modulation'of the previously steady current will result.

Of course, the function generator can be programmed to represent anyvariation from steady state flow and this signal can be impressed at anyplace along the analog model corresponding to where the variation isintroduced in the parent system. For example, it could be programmed torepresent predicted variations in compressor discharge pressure and beintroduced as the reference signal to the differential amplifier 26.

Also, in programming the opaque tape 36 care should be taken to insurethat nonlinearities due to uneven light distribution, nonuniformtransmission of the cylinder material, and nonlinear response of thephotocell will not result. This can be done by programming (i.e.,placing the tape strips) directly in accordance with the photocelloutput voltage while indexing the cylinder.

FLOW SYSTEM ANALOG Having described the various components of anelectrical analog model and their relation to corresponding componentsin the parent flow system, it is necessary to describe the connectionand operation of these components in the electrical analog model flowsystem analog. In this way, the effects of variation of an electricalquality anywhere in the electrical model, upon electrical qualitieselsewhere in the model, will be proportional in a known manner to theeffect of a corresponding variation in a flow quality upon flowqualities elsewhere in the flow system. The electrical variations needonly be measured and converted by the proper conversion factor to givethe corresponding flow variations. Thus, analogous flow conditions areimposed on the analog model and direct measurements are then possible asto system response to these flow conditions.

Since the fluid system analog is made up of various individual componentanalogs used in combinations, it is necessary that each of thesecomponents be adjusted to utilize the same basic analogies and the sameor at least compatible basic scaling factors. For example, if voltage isproportional to pressure squared and current is proportional to massflow, it is usually convenient to have the same analogies throughout thetotal system; further, it is usually convenient to keep theproportionality constants between voltage and pressure and current andflow the same for each line section, for the compressor analogs, theregulator valves, etc. While it is convenient to keep these factorsconstant throughout the system, special transformations may be used topermit variation of these facill tors at convenient points in thesystem, and even to permit changing the basic analogies. Of course, theanalog is useful for studying pipeline or piping flow even if nocompressors or regulators are involved, when, for example, well headpressure is sufficient to remove the gas and a block valve may be usedto control discharge of the gas into another system. Also, the analog isapplicable to virtually any form of closed, onedimensional flow regime,such as hydraulic systems wherein the tubing and hoses and even the ductsystems can be simulated.

With reference to FIGS. 2, 3 and 4, the analog model shown thereinoperates as follows. A system input pressure (Pl) set point is selectedfor the fluid system. This may be the discharge pressure from anotherpipeline or from a storage reservoir. An analogous voltage (21) for thesquare of this pressure is set by a battery B2. The voltage chosen willdepend primarily on the range of pressures to be simulated and theminimum and maximum voltage required for the electrical system. Once thevoltage is selected, the conversion factor a can be determined from theformula p =ae and then used to convert pressure to corresponding voltagethroughout the system. Voltages proportional to the discharge pressuresquared of compressor stations 11 and 16 are then selected as referencevoltages and each provides the reference signal input for the differenceamplifiers 26 of the compressor station analogs. The actual dischargevoltages e2 and 25 are then compared by the difference amplifiers withtheir respective reference voltages to produce an error signal which isused to control the output level of the controlled level amplifier 27.Capacitor pump 24 thru-put is thus controlled so that discharge voltagese2 and 25 are proportional to compressor station discharge pressures(P2, P) squared.

The compressor analog output voltages e2 and 25, respectively, set theinput voltages for the delay lines representing the pipeline sections 12and 17. The voltage drop across each delay line 20 is set to representand be proportional to the pressure drop across a corresponding pipelinesection, and the value of C1 is chosen according to formula above for agiven voltage. Regulator station analog 29 converts input voltage at e3corresponding to pressure P3 squared to a constant lower value e3proportional to regulator station 14 output pressure P3 squared.Regulator station analog 30 converts the output of the terminal delayline i to voltage e7 proportional to regulator station 18 outputpressure (P7) squared. The output voltage of the regulator stationanalog is set by setting the reference voltage input to differenceamplifier 32 through potentiometer P2 to a reference voltageproportional to the regulator station output.

With the setup described above, an electrical analog model of the staticflow of gas in the system of FIG. 1 has been built. However, since theanalogy and the nonlinear electrical circuitry requirements developedand used were based on a fluid system including transient flow,electrical transients corresponding to the flow transients can beimposed on the analog model, and then the response of the electricalquantities through the model to the electrical transients can beobserved and measured. These electrical values measured will bear aknown relationship to corresponding flow values. As described earlier,the transients are simulated by properly programming the tape 36 of theload function generator 33. The analog model is modulated by thesetransients at the regulator station analog output by flow modulator 40.

It can be seen that the analog model disclosed herein provides a meanswhich can be used to investigate the physical phenomena of transientflow in pipelines, in a manner which will permit the expression of thesephenomena in terms of pipeline operation control and design. It providesa means for predicting pipeline operating conditions based upon the flowresponse characteristics of the pipeline system operating under variableload conditions. The individual analog components (.such as compressorand regulator stations) are coupled together on a block-by-blockrepresentation of the parent pipeline system and once the response ofthese individual components have been simulated, interaction of thesecomponent responses, or transient coupling, is automatically obtained togive adequate simulation of the response of the parent piping system.Thus, all data or operating characteristics of the pipeline arevirtually immediately obtainable on the analog model in direct analogyto that which would be observed on an actual pipeline installation. Thisdata can be used in designing, building, operating, and maintaining thetransmission system economically and efficiently, and in instructingothers in the proper techniques for accomplishing these objectives.

Although the above description has been directed to developing nonlinearelectrical analog circuitry for steady state and transient flowevaluation, it should be recognized that by using the same principles toevolve the necessary analogies, a linear transient only analog model canbe built. If the average conditions of steady-state flow and pressureare defined, then the circuit component sizes can be defined by theseconditions and an analog built which would define transient response forthat combination ofline and steady flow parameters. Of course, for otheraverage flow conditions different values in the R-C delay line wouldhave to be used. Although the use of the linear transient only analogwould be more limited than the nonlinear analog, it could be used as avaluable tool in checking concepts of the more sophisticated nonlinearanalog, and in supplying data quickly against which the nonlinear analogcould be checked.

From the foregoing, it will be seen that this invention is one welladapted to attain all of the ends and objects hereinabove set forth,together with other advantages which are obvious and which are inherentto the apparatus and method.

It will be understood that certain features and subcombinations are ofutility and may be employed without reference to other features andsubcombinations. This is contemplated by and is within the scope of theclaims.

As many possible embodiments may be made of the invention withoutdeparting from the scope thereof, it is to be understood that all matterherein set forth or shown in the accompanying drawings is to beinterpreted as illustrative and not in a limiting sense.

The invention having been described, what we claim is:

1. An analog system for electrically simulating the flow of fluidthrough a pipeline system wherein fluid is being conducted underpressure, for defining flow characteristics therein, including theeffect of flow transients on said flow, and wherein said pipeline systemincludes at least one pipeline section having an inlet connected to asource of said fluid and a load connected to an outlet of said pipelinesection for withdrawal and use of said fluid, said analog systemcomprising, in combination: a source of electrical energy for simulatingthe source of fluid at said inlet by providing an electrical analogsignal having electrical values proportional to flow values at saidinlet, including fluid pressure and rate of flow of the fluid at theinlet said electrical analog signal having a voltage proportional to oneof said flow values and an electrical current proportional to another ofsaid flow values; pipeline section analog means coupled at its inputterminal to said source for receipt of said electrical analog signal andsimulating said pipeline section, said pipeline section analog meansresponding to said electrical values of said electrical analog signaland causing variations thereof proportional to changes in said flowvalues of fluid conducted through said pipeline section and storing atleast a part of the energy supplied from said source to said pipelinesection analog means to simulate fluid pack, the electrical values ofsaid electrical analog signal at the output terminal of said pipelinesection analog simulating flow values at said outlet; and load transientanalog means for simulating said load by providing a variable electricalsignal proportional to flow transients the effect of which on fluid flowto said pipeline section is to be simulated, said transient analog meansbeing connected to the output terminal of said pipeline section analogmeans and modulating said electrical analog signal with said variableelectrical signal in a manner analogous to the manner in which fluidflow is subjected to flow transients at said outlet, whereby changeswhich can be measured in electrical values in the electrical analogsystem in response to said variable electrical signal, correspond tochanges in the flow values of the flow system in response to flowtransients.

2. The combination of claim 1 wherein said pipeline system to beanaloged includes at least one compressor station connected between saidinlet and said outlet for maintaining the fluid at sufficient pressuresfor transportation and utilization, and said analog system furtherincludes means connected between said source of electrical energy andsaid pipelinc section analog means for electrically simulating thecompressor station and its effects on fluid pressure and flow.

3. The combination of claim 1 wherein said pipeline system to beanaloged includes at least one regulator connected between said inletand said outlet for maintaining fluid conducted to a load atsubstantially constant pressure despite varying flow rates, and saidanalog system further includes means connected between said pipelinesection analog means and said load transient analog means forelectrically simulating the regulator and its effects on fluid pressureand flow.

4. The combination of claim 2 wherein said pipeline system to beanaloged includes at least one regulator connected between saidcompressor station and said outlet for maintaining fluid conducted to aload at substantially constant pressure despite varying flow rates, andsaid analog system further includes means connected between saidpipeline section analog means and said load transient analog means forelectrically simulating the regulator and its effects on fluid pressureand flow.

5. The combination of claim 4 wherein said compressor station simulatingmeans includes means converting said electrical analog signal from avalue proportional to compressor station suction pressure to a valueproportional to compressor discharge pressure, and said regulatorsimulating means includes means for converting said electrical analogsignal from a value proportional to fluid pressure at a pipelinetermination to a lesser constant value for electrically simulatingpressure regulation of the regulator in response to varying loads.

6. The analog of claim 5 wherein fluid pressure squared is proportionalto and simulated by an electrical voltage and the fluid mass flow isproportional to and simulated by an electrical current throughout theanalog.

7. The analog of claim 6 wherein said electrical analog signal includesa direct current voltage proportional to pipeline inlet pressuresquared, and said pipeline section analog means includes a delay linefor simulating fluid flow response through said pipeline section, saiddelay line including a nonlinearresistance means, the resistance ofwhich is proportional to the current passing through it to simulate theeffect of pipeline friction on fluid flow, and nonlinear capacitancemeans the capacitance of which is inversely proportional to the squareroot of the impressed voltage for simulating pipeline storage responsesto transient flow.

8. An analog for electrically simulating the flow of fluid through apipeline system conducting fluid under pressure, for defining flowcharacteristics therein, including the effects of flow transients onsaid flow, said pipeline system including a pipeline section having aninlet connected to a source of fluid and an outlet connected to a load,said analog comprising, in combination: means providing a firstelectrical signal having values proportional to flow qualities of thefluid at the inlet of said pipeline section; means for simulating saidpipeline section by responding to said first electrical signal andconverting it to a second electrical signal having values proportionalto flow qualities of the fluid at the outlet of said pipeline section,including meanssimulating the effects of pipeline friction and fluidpack on pipeline flow; means providing a third electrical signalproportional to flow transients the effect of which on fluid flow is tobe simulated; and means for modulating said second electrical signalwith said third electrical signal in a manner analogous to the manner inwhich the fluid flow in the pipeline is subjected to flow transients,whereby changes which can be measured in electrical qualities of theelectrical analog in response to said third electrical signal,corresponding to changes in the flow qualities of the flow system inresponse to flow transients.

9. A compressor station analog for simulating a compressor station alonga fluid transmission system, said analog compris ing, in combination: aninput terminal adapted to be connected to a source of electrical voltageproportional to compressor station suction pressure; an output terminaladapted to be connected to a variable load representing flow transientsat compressor station discharge; and means connected between said inputterminal and output terminal and responding to the variations in saidvariable load when connected to said output terminal to convert saidelectrical voltage when said input terminal is connected to said sourceto a value at said output terminal proportional to compressor stationdischarge pressure.

10. The analog of claim 9 wherein said means connected between saidinput terminal and said output terminal includes a capacitor pumpconnected to said input terminal, said pump having a capacitor and firstand second rectifiers connected to said capacitor to form a T-sectionmeans generating an alternating current driving signal for driving saidcapacitor pump; and means coupling said driving signal generating meansto said capacitor pump, said last mentioned means responding to changesin the voltage at said to vary said driving signal an amount sufflcientto maintain said output terminal voltage proportional to compressordischarge pressure.

11. A regulator electrical analog for simulating a regulator connectedin a fluid flow system and providing constant discharge pressure despitevarying mass flow in said system, comprising, in combination: an inputfor receipt of an electrical signal ofa varying value which isproportional to fluid pressure at the inlet to said regulator; variableimpedance means connected to said input and converting said value ofsaid electrical signal to a lesser constant value at an output forelectrically simulating pressure regulation of the regulator in responseto varying loads; an electrical load connected to such output andsimulating a fluid load requiring a constant pressure despite varyingmass flow, and means connected to said output and to said variableimpedance means and responding to said electrical signal at said outputfor causing said variable impedance means to automatically vary toprovide said lesser constant value.

12. Apparatus adapted to be connected in a fluid flow system electricalanalog for simulating flow transients including load withdrawal demandson the fluid system and impressing said transients on the electricalanalog of said system, and wherein said electrical analog is provided byan electrical signal having electrical values corresponding to flowvalues in said flow system, said apparatus comprising, in combination: afunction generator providing an electrical current output having a waveform, the amplitude of which is proportional to the volume of fluidwithdrawal and the duration of which is proportional to the period ofwithdrawal, and flow modulation means connected to said functiongenerator for receipt of said electrical current output, the output ofsaid flow modulation means adapted to be connected to said electricalanalog for modulating said electrical signal with an electrical currentwhich simulates said flow transient.

13. The apparatus of claim 12 wherein said function generator includes asource of light, a light sensor responding to said light to provide saidelectrical current output; an opaque program tape extending through thepath of light between said light and said light sensor, said tape beingprogrammed to simulate volume of fluid utilization; and means for movingsaid tape through said path at a rate so that said electrical out putsimulates the amount and the rate of fluid withdrawal from said fluidflow system.

14. A method of simulating fluid flow through at least a portion offluid flow system conducting flluid under pressure for defining flowcharacteristics therein including the effect of flow transients on saidflow, by an electrical analog wherein electrical values are related toflow values in said fluid flow system comprising the steps of:generating a first electrical signal having an electrical valueproportional to portion input pressures and another value proportionalto the rate of fluid flow at the input of said fluid flow system;causing said first electrical signal to be altered on amountproportional to the pressure drop of the fluid due to friction andinertia as said fluid flows through said portion and causing said firstelectrical signal to be altered an amount proportional to the change inrate of flow of fluid from the inlet of said portion to the outlet ofsaid portion; utilizing said first electrical signal to store electricalenergy in an amount proportional to the fluid pack capacity of saidportion; generating a second electrical signal proportional to flowtransients, the effect of which on fluid flow is to be simulated; andmodulating said first electrical signal with said second signal tosimulate the effect of flow transients on fluid flow in the flow systemwhereby changes which can be measured in the electrical values of thesaid first electrical signal in response to said second electricalsignal, correspond to changes in the flow values of the flow system inresponse to flow transients 15. The method of claim 14 wherein said flowsystem is a transmission system including at least one compressorstation along a pipeline for maintaining the fluid at sufficientpressures for transportation, and further including the step ofincreasing said first electrical signal from a value proportional tocompressor station suction pressure to a value proportional tocompressor station discharge pressure.

16. The method of claim 15 wherein said flow system is a transmissionsystem including at least one regulator for maintaining fluid conductedfrom a pipeline to a load or from a source at substantially constantpressure despite varying flow rates, and further including the step ofdecreasing said first electrical signal from a value proportional toregulator station output pressure.

17. The method of claim 15 wherein said flow system is a transmissionsystem including at least one regulator for maintaining fluid conductedfrom a pipeline to a load or from a source at substantially constantpressure despite varying flow rates, and further including the step ofdecreasing said first electrical signal from a value proportional toregulator input pressure to a value proportional to regulator stationoutput pressure.

18. The method of claim 14 wherein said second electrical signalincludes electrical quantities proportional to the rate and quantity offluid utilization by said load.

1. An analog system for electrically simulating the flow of fluidthrough a pipeline system wherein fluid is being conducted underpressure, for defining flow characteristics therein, including theeffect of flow transients on said flow, and wherein said pipeline systemincludes at least one pipeline section having an inlet connected to asource of said fluid and a load connected to an outlet of said pipelinesection for withdrawal and use of said fluid, said analog systemcomprising, in combination: a source of electrical energy for simulatingthe source of fluid at said inlet by providing an electrical analogsignal having electrical values proportional to flow values at saidinlet, including fluid pressure and rate of flow of the fluid at theinlet said electrical analog signal having a voltage proportional to oneof said flow values and an electrical current proportional to another ofsaid flow values; pipeline section analog means coupled at its inputterminal to said source for receipt of said electrical analog signal andsimulating said pipeline sectiOn, said pipeline section analog meansresponding to said electrical values of said electrical analog signaland causing variations thereof proportional to changes in said flowvalues of fluid conducted through said pipeline section and storing atleast a part of the energy supplied from said source to said pipelinesection analog means to simulate fluid pack, the electrical values ofsaid electrical analog signal at the output terminal of said pipelinesection analog simulating flow values at said outlet; and load transientanalog means for simulating said load by providing a variable electricalsignal proportional to flow transients the effect of which on fluid flowto said pipeline section is to be simulated, said transient analog meansbeing connected to the output terminal of said pipeline section analogmeans and modulating said electrical analog signal with said variableelectrical signal in a manner analogous to the manner in which fluidflow is subjected to flow transients at said outlet, whereby changeswhich can be measured in electrical values in the electrical analogsystem in response to said variable electrical signal, correspond tochanges in the flow values of the flow system in response to flowtransients.
 2. The combination of claim 1 wherein said pipeline systemto be analoged includes at least one compressor station connectedbetween said inlet and said outlet for maintaining the fluid atsufficient pressures for transportation and utilization, and said analogsystem further includes means connected between said source ofelectrical energy and said pipeline section analog means forelectrically simulating the compressor station and its effects on fluidpressure and flow.
 3. The combination of claim 1 wherein said pipelinesystem to be analoged includes at least one regulator connected betweensaid inlet and said outlet for maintaining fluid conducted to a load atsubstantially constant pressure despite varying flow rates, and saidanalog system further includes means connected between said pipelinesection analog means and said load transient analog means forelectrically simulating the regulator and its effects on fluid pressureand flow.
 4. The combination of claim 2 wherein said pipeline system tobe analoged includes at least one regulator connected between saidcompressor station and said outlet for maintaining fluid conducted to aload at substantially constant pressure despite varying flow rates, andsaid analog system further includes means connected between saidpipeline section analog means and said load transient analog means forelectrically simulating the regulator and its effects on fluid pressureand flow.
 5. The combination of claim 4 wherein said compressor stationsimulating means includes means converting said electrical analog signalfrom a value proportional to compressor station suction pressure to avalue proportional to compressor discharge pressure, and said regulatorsimulating means includes means for converting said electrical analogsignal from a value proportional to fluid pressure at a pipelinetermination to a lesser constant value for electrically simulatingpressure regulation of the regulator in response to varying loads. 6.The analog of claim 5 wherein fluid pressure squared is proportional toand simulated by an electrical voltage and the fluid mass flow isproportional to and simulated by an electrical current throughout theanalog.
 7. The analog of claim 6 wherein said electrical analog signalincludes a direct current voltage proportional to pipeline inletpressure squared, and said pipeline section analog means includes adelay line for simulating fluid flow response through said pipelinesection, said delay line including a nonlinear resistance means, theresistance of which is proportional to the current passing through it tosimulate the effect of pipeline friction on fluid flow, and nonlinearcapacitance means the capacitance of which is inversely proportional tothe square rooT of the impressed voltage for simulating pipeline storageresponses to transient flow.
 8. An analog for electrically simulatingthe flow of fluid through a pipeline system conducting fluid underpressure, for defining flow characteristics therein, including theeffects of flow transients on said flow, said pipeline system includinga pipeline section having an inlet connected to a source of fluid and anoutlet connected to a load, said analog comprising, in combination:means providing a first electrical signal having values proportional toflow qualities of the fluid at the inlet of said pipeline section; meansfor simulating said pipeline section by responding to said firstelectrical signal and converting it to a second electrical signal havingvalues proportional to flow qualities of the fluid at the outlet of saidpipeline section, including means simulating the effects of pipelinefriction and fluid pack on pipeline flow; means providing a thirdelectrical signal proportional to flow transients the effect of which onfluid flow is to be simulated; and means for modulating said secondelectrical signal with said third electrical signal in a manneranalogous to the manner in which the fluid flow in the pipeline issubjected to flow transients, whereby changes which can be measured inelectrical qualities of the electrical analog in response to said thirdelectrical signal, corresponding to changes in the flow qualities of theflow system in response to flow transients.
 9. A compressor stationanalog for simulating a compressor station along a fluid transmissionsystem, said analog comprising, in combination: an input terminaladapted to be connected to a source of electrical voltage proportionalto compressor station suction pressure; an output terminal adapted to beconnected to a variable load representing flow transients at compressorstation discharge; and means connected between said input terminal andoutput terminal and responding to the variations in said variable loadwhen connected to said output terminal to convert said electricalvoltage when said input terminal is connected to said source to a valueat said output terminal proportional to compressor station dischargepressure.
 10. The analog of claim 9 wherein said means connected betweensaid input terminal and said output terminal includes a capacitor pumpconnected to said input terminal, said pump having a capacitor and firstand second rectifiers connected to said capacitor to form a T-sectionmeans generating an alternating current driving signal for driving saidcapacitor pump; and means coupling said driving signal generating meansto said capacitor pump, said last mentioned means responding to changesin the voltage at said to vary said driving signal an amount sufficientto maintain said output terminal voltage proportional to compressordischarge pressure.
 11. A regulator electrical analog for simulating aregulator connected in a fluid flow system and providing constantdischarge pressure despite varying mass flow in said system, comprising,in combination: an input for receipt of an electrical signal of avarying value which is proportional to fluid pressure at the inlet tosaid regulator; variable impedance means connected to said input andconverting said value of said electrical signal to a lesser constantvalue at an output for electrically simulating pressure regulation ofthe regulator in response to varying loads; an electrical load connectedto such output and simulating a fluid load requiring a constant pressuredespite varying mass flow, and means connected to said output and tosaid variable impedance means and responding to said electrical signalat said output for causing said variable impedance means toautomatically vary to provide said lesser constant value.
 12. Apparatusadapted to be connected in a fluid flow system electrical analog forsimulating flow transients including load withdrawal demands on thefluid system and impressing said transients on the electrical aNalog ofsaid system, and wherein said electrical analog is provided by anelectrical signal having electrical values corresponding to flow valuesin said flow system, said apparatus comprising, in combination: afunction generator providing an electrical current output having a waveform, the amplitude of which is proportional to the volume of fluidwithdrawal and the duration of which is proportional to the period ofwithdrawal, and flow modulation means connected to said functiongenerator for receipt of said electrical current output, the output ofsaid flow modulation means adapted to be connected to said electricalanalog for modulating said electrical signal with an electrical currentwhich simulates said flow transient.
 13. The apparatus of claim 12wherein said function generator includes a source of light, a lightsensor responding to said light to provide said electrical currentoutput; an opaque program tape extending through the path of lightbetween said light and said light sensor, said tape being programmed tosimulate volume of fluid utilization; and means for moving said tapethrough said path at a rate so that said electrical output simulates theamount and the rate of fluid withdrawal from said fluid flow system. 14.A method of simulating fluid flow through at least a portion of fluidflow system conducting fluid under pressure for defining flowcharacteristics therein including the effect of flow transients on saidflow, by an electrical analog wherein electrical values are related toflow values in said fluid flow system comprising the steps of:generating a first electrical signal having an electrical valueproportional to portion input pressures and another value proportionalto the rate of fluid flow at the input of said fluid flow system;causing said first electrical signal to be altered on amountproportional to the pressure drop of the fluid due to friction andinertia as said fluid flows through said portion and causing said firstelectrical signal to be altered an amount proportional to the change inrate of flow of fluid from the inlet of said portion to the outlet ofsaid portion; utilizing said first electrical signal to store electricalenergy in an amount proportional to the fluid pack capacity of saidportion; generating a second electrical signal proportional to flowtransients, the effect of which on fluid flow is to be simulated; andmodulating said first electrical signal with said second signal tosimulate the effect of flow transients on fluid flow in the flow systemwhereby changes which can be measured in the electrical values of thesaid first electrical signal in response to said second electricalsignal, correspond to changes in the flow values of the flow system inresponse to flow transients.
 15. The method of claim 14 wherein saidflow system is a transmission system including at least one compressorstation along a pipeline for maintaining the fluid at sufficientpressures for transportation, and further including the step ofincreasing said first electrical signal from a value proportional tocompressor station suction pressure to a value proportional tocompressor station discharge pressure.
 16. The method of claim 15wherein said flow system is a transmission system including at least oneregulator for maintaining fluid conducted from a pipeline to a load orfrom a source at substantially constant pressure despite varying flowrates, and further including the step of decreasing said firstelectrical signal from a value proportional to regulator station outputpressure.
 17. The method of claim 15 wherein said flow system is atransmission system including at least one regulator for maintainingfluid conducted from a pipeline to a load or from a source atsubstantially constant pressure despite varying flow rates, and furtherincluding the step of decreasing said first electrical signal from avalue proportional to regulator input pressure to a value proportionalto regulator station output pressure.
 18. The method of claim 14 whereinsaid second electrical signal includes electrical quantitiesproportional to the rate and quantity of fluid utilization by said load.